Lesson 4_Laws of Exponents incomplete.pptx

Lesson 4_Laws of Exponents incomplete.pptx

1. Laws of Exponents LESSON 4

2. What is an exponent? An exponent is a small number written on the right side of a coefficient. It tells how many times you multiply the coefficient by itself. It also called Power or Indices . When you come across the expression 3².Here, we say that 3 is the base and 2 is the exponent, which means 3 times 3 is equal to 9. both ways are equal to 9 In algebra it is written as 3² = (3)(3) or 3² = (3∙3)

3. What is an exponent? 3 2 can be read as: x 3 can be read as: three squared three with the power of two three raise to the second power three raise to the power of two x cube x with the power of 3 x raise to the third power x raise to the power of 3

4. Activity 1: Expand Me! Exponential Form Expanded Form Exponential Form Expanded Form 1. x 3 y 2 (x∙x∙x) (y∙y) 4. y 3   2. a 4   5. a 2 b 4   3. x 4   6. x 2 y 2  

5. A. Product Rule a m ∙ a n = a m+n If we multiply expressions with the same base we simply add the exponents and copy the base. (2 3 )(2 4 )= (2∙2)∙(2∙2∙2∙2) (2 3 ) (2 4 ) = 2 3+4=7

6. A. Product Rule a m ∙ a n = a m+n If we multiply expressions with the same base we simply add the exponents and copy the base. Examples: (x 3 ) (x 11 ) =x 3 + 8 =x 11 Thus,(x 3 ) (x 8 )= x 11 2. (a 2 b 3 ) (a 5 b) = a 2+5 b 3+1 = a 2+5=7 b 3+1=4 = a 7 b 4

7. TRY THESE! a m ∙ a n = a m+n Practice Exercises! Simplify the expressions below by applying the product rule. 1. (x 4 ) (x 6 ) = 2. (3a 8 ) (4a 6 ) (2a 4 ) = 3. (4x 6 y 4 ) (3x 2 y 3 ) =

8. B. Quotient Rule   If the greater exponent is in the denominator, put the difference in the denominator this will help avoid negative exponents .        

9. Try These!

10. C. Power Rule   lf numbers a and b and any positive integer , m and n. It means to raise a power to a power, you just need to multiply the exponents directly and copy the base.        

11. Try These!

12. C.1 Product-to-Power Rule   For, all real numbers a and b , and any positive integers m, n, and p. It means to raise each factor inside the parentheses to the given exponent outside the parentheses.      

13. Try These!

14. C.2 Quotient-to-Power Rule For, all real numbers a and b , and any positive integers m, n, and p. It means to raise each factor inside the parentheses to the given exponent outside the parentheses.        

15. Try These!

16. D. Negative Exponent Rule When the expressions contain negative exponent, it can be written in its reciprocal form and the exponent becomes positive. It can also be simplify in this way, when the expression with negative exponent is in numerator transfer the expression to the denominator and the exponent becomes positive. Also, the expression with negative exponent is in the denominator transfer the expression to the numerator and the exponent becomes positive.      

17. Try These!

18. E. Zero Exponent Rule Any expressions when raise to zero power is always equal to 1.      

19. Try These!

20. ACTIVITY

21. Law 1: Product Rule

22. Law 2: Quotient Rule

23. Law 3: Power Rule

24. Last Batch of Practice Problems

25. Last Batch of Practice Problems